Question

The point on the terminal side of θ = -3 pi/ 4 that has an x coordinate of -1

Answer 1

\[x=r \cos \theta \]
\[r \cos \frac{ -3 \pi }{ 4 }=-1\]
\[r \cos \frac{ 3 \pi }{ 4 }=-1\]
\[r \cos \left( \pi-\frac{ \pi }{ 4 } \right)=-1\]
\[-r \cos \frac{ \pi }{ 4 }=-1\]
\[r*\frac{ 1 }{\sqrt{2} }=1,r=\sqrt{2}\]
\[y=r \sin \theta=\sqrt{2}\sin \frac{ -3 \pi }{ 4 }=-\sqrt{2}\sin \frac{ 3\pi }{ 4 }=-\sqrt{2}\sin \left( \pi-\frac{ \pi }{ 4 } \right)\]
\[or~y=-\sqrt{2}\sin \frac{ \pi }{ 4 }=-\sqrt{2}*\frac{ 1 }{\sqrt{2} }=-1\]
so point is (-1,-1)